Modelling physical systems with ODEs
The SIR model has proved incredibly useful in predicting the evolution of certain categories of infectious outbreaks and serves as our introduction to modeling systems with ODEs.
Well, all hell has broken loose. The zomb-pocalypse is happening!
Using numerical methods to solve ordinary differential equations.
Using Verlet's method to solve the equation of motion of a pendulum, we will compare the true period to the approximated value given by the small-angle approximation.
A pendulum, made of a magnet, is moving over a surface with three fixed magnets. In this lab, we will determine the trajectory of the magnetic pendulum and explore some of its chaotic behaviour.
Now that we have a working magnetic pendulum model, let's create a map that shows where the pendulum terminates based on its starting position.
"Change is the only constant" - Heraclitus
Ordinary Differential Equations (ODEs) can be used to model any process involving rates of change. Given Heraclitus' insight, you can see why ODEs are such an important tool in mathematical modeling.